ca. 300 B.C.
Nothing certain is known about the personal life of Euclid, but he may have taught mathematics at the court of Ptolemy I in Alexandria in Egypt. Euclid’s fame rests on the Elements, a geometry textbook that used the knowledge and achievements of preceding mathematicians but then moved beyond them.
Some historians doubt that Euclid actually wrote all the works that are attributed to him. For example, some of the ideas in the Elements seem to have originated with a mathematician named Eudoxus. However, Euclid’s Elements was so comprehensive and so well-organized and clearly stated that it was acclaimed around the world. It was translated into Latin, Hebrew, Arabic, and many other languages, and it remained the ultimate authority on geometry until the 1800s. High school students today still begin their work in geometry by studying the basic principles that Euclid established.
The Elements consists of 13 books, and deals primarily with plane geometry, solid geometry, proportion, and the theory of numbers. In fact, plane geometry—the branch of geometry that deeds with two-dimensional figures—is still called Euclidean geometry in honor of Euclid’s work.
In the Elements, Euclid presented the mathematical concepts in an organized way, much more systematically than had ever been done before. He set forth a series of elementary propositions, which he called “elements,” and then showed how more complicated propositions could be derived from the elementary ones.
In this important work, Euclid does not try to prove that his premises, or axioms, are true. He simply assumes that they are true and then proceeds through an orderly sequence of certain geometrical conclusions. This thinking process—called deduction—was developed and used by Euclid and other Greek scientists and philosophers, and it was itself one of the most important contributions of ancient Greek science. The use of deduction to proceed logically from premises to conclusions became one of the foundations of scientific thinking.
Other surviving works believed to be by Euclid include Data, another work on geometry; Optics, a study of perspective; and Phenomena, a textbook on astronomy. Euclid also may have written two works exploring the mathematical basis of music.